# Angle functions - Determine the angle needed to slide one curve into another

Working on the angle functions, there's a problem that says:

Determine the angle needed to slide the $\cos$ curve into the $\sin$ curve.

The solution is described as

$\cos\Big(x - \dfrac{\pi}{2}\Big) = \sin(x)$

Which means, the needed angle is $-\dfrac{\pi}{2}$.

How do I know (or calculate) that particular angle?

And how do I do the same when determining the angle needed to slide one curve of any angle function to any curve of any other angle function?

The functions I know of are $\sin$, $\cos$, $\tan$ and $\cot$.

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Do you know what the graph of $y=\sin x$ looks like? Ditto, $y=\cos x$? From looking at the graphs, you should be able to see how far you have to move one to have it coincide with the other.
Without a graph? Well. do you know the addition formulas, $\sin(a+b)=\sin a\cos b+\cos a\sin b$ and the like? If you want just $\cos a$ on the right you have to take $b$ so the $\cos b$ on the right goes away, so take $b=\pi/2$, so $\sin(a+(\pi/2))=\cos a$. Alternatively, do you know the definitions of the trig functions in terms of points on the unit circle? – Gerry Myerson May 19 '12 at 12:47
Without a graph? Well. do you know the addition formulas, $\sin(a+b)=\sin a\cos b+\cos a\sin b$ and the like? If you want just $\cos a$ on the right you have to take $b$ so the $\cos b$ on the right goes away, so take $b=\pi/2$, so $\sin(a+(\pi/2))=\cos a$. Alternatively, do you know the definitions of the trig functions in terms of points on the unit circle? – Gerry Myerson May 19 '12 at 12:50
No, didn't know about those formulas. How do they apply to the other functions ($\tan$ and $\cot$)? Maybe you could expand on that in your answer? About the unit circle, I got some notion of how that works, but I'm not entirely comfortable there. – Miroslav Cetojevic May 19 '12 at 12:57